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# Topological Shiba bands in artificial spin chains on superconductors

## Abstract

A major challenge in developing topological superconductors for implementing topological quantum computing is their characterization and control. It has been proposed that a p-wave-gapped topological superconductor can be fabricated with single-atom precision by assembling chains of magnetic atoms on s-wave superconductors with spin–orbit coupling. Here we analyse Bogoliubov quasiparticle interference in Mn chains, constructed atom by atom on Nb(110), and reveal the formation of multi-orbital Shiba bands using momentum-resolved measurements. We find evidence that one band features a topologically non-trivial p-wave gap, as inferred from its shape and particle–hole asymmetric intensity. Our work is an important step towards a distinct experimental determination of topological phases in multi-orbital systems by bulk electron band structure properties only.

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## Data availability

Data that support the findings of this paper are available from the corresponding author upon reasonable request. Source data are provided with this paper.

## Code availability

The analysis codes that support the findings of the study are available from the corresponding author upon reasonable request.

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## Acknowledgements

L.S., P.B., T.P., J.W. and R.W. gratefully acknowledge funding by the Cluster of Excellence ‘Advanced Imaging of Matter’ (EXC 2056—project ID 390715994) of the Deutsche Forschungsgemeinschaft (DFG). L.S., P.B., J.W. and R.W. acknowledge support by the SFB 925–B9 ‘Light induced dynamics and control of correlated quantum systems’ of the Deutsche Forschungsgemeinschaft (DFG). T.P. acknowledges support by the DFG (project no. 420120155). R.W. acknowledges funding by the European Union via ERC Advanced Grant ADMIRE (project no. 786020). S.R. acknowledges support from the Australian Research Council (DP200101118). We thank D. K. Morr, H. Jeschke and L. Rózsa for helpful discussions. T.P. thanks F. Pientka for clarifying remarks.

## Author information

Authors

### Contributions

L.S., P.B., R.W. and J.W. conceived the experiments. L.S. and P.B. performed the measurements and analysed the experimental data together with J.W. T.P. derived the effective low-energy Shiba model. L.S. performed the numerical simulations using the effective low-energy Shiba model and the fitting to the experimental data. D.C., E.M. and S.R. performed numerical simulations, which were essential for the understanding of the system. L.S. prepared the figures. L.S. and J.W. wrote the manuscript. All authors contributed to the discussions and to correcting the manuscript.

### Corresponding author

Correspondence to Jens Wiebe.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature Physics thanks Yukio Hasegawa and Jose Pascual for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Supplementary information

### Supplementary Information

Supplementary Figs. 1–7, details of the experimental procedures, the QPI analysis and the theoretical model.

## Source data

### Source Data Fig. 1

Source data Fig 1.

### Source Data Fig. 2

Source data Fig 2.

### Source Data Fig. 3

Source data Fig 3.

### Source Data Fig. 4

Source data Fig 4.

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Schneider, L., Beck, P., Posske, T. et al. Topological Shiba bands in artificial spin chains on superconductors. Nat. Phys. (2021). https://doi.org/10.1038/s41567-021-01234-y